The 12-point motion was tabled by Councillor Carolyn Healy, a cabinet member in the borough’s Labour administration, and supported across the chamber.
Liberal Democrat councillor Thomas Janke voted in favour but said it did not go far enough, and proposed an amendment, which was defeated, that would have moved the zero-carbon deadline five years forward.
Telford & Wrekin is now one of nearly 200 UK local authorities to have declared a climate emergency.
Councillor Healy’s motion also committed the council to measure and track its own carbon footprint, ditch disposable plastics and support plastic-free projects locally and nationally.
She said: “I represent the Ironbridge Gorge ward, a place we rightly celebrate as the birthplace of industry, where innovation and creativity helped shape the modern world.
“But we now know industrialisation is having a catastrophic effect on our climate and threatens our very existence.”
She referred to the 2018 report by the Intergovernmental Panel on Climate Change, which called for “ambitious action from national, sub-national organisations and authorities, citizens and the private sector”.
Councillor Healy said declaring a climate emergency would recognise “the seriousness of the issue and the urgency to take action now”.
“We also recognise that plastic pollution is harming ecosystems at a time when species are struggling to adapt to climate change,” she added.
But she warned this would need to be done in a way that “does not disadvantage our most vulnerable residents – we need to take people with us on this journey”.
Councillor Janke said he and his party welcomed the original motion.
The Newport South and East councillor added: “We do believe, however, this carbon neutrality target of 2030 is not ambitious enough.
“Climate change is the single biggest existential threat to our species.
“Our children and grandchildren are expecting us to pick up the baton and fight for them.
“We are 11 years from the target in the original motion, by which time it might already be too late.”
He pointed out that the neighbouring council areas of Wolverhampton and Cannock Chase had set themselves a 2028 target, and asked Telford and Wrekin members to consider “at least 2025”.
Had it passed, Councillor Janke’s amendment would also have committed the council to co-opt experts to help with the zero-carbon campaign and pro-actively encourage residents to find alternatives to single-use plastic products.
Replying, Councillor Healy said 2030 was a “deadline, not a target”.
She added: “If we can meet it earlier, we will.”
Conservative Adrian Lawrence supported Councillor Healy’s motion and said it was important the council “lead by example”.
But the Muxton ward councillor added that the council’s direct impact would be small compared to the general population.
“That said, the council is in a position to have a strong influence,” he said.
“We have our development proposals, residential and commercial. As an example, we could condition each residential development to have charging points, which would contribute to a change.
“The council has a fleet of electric vehicles. We could work with our procurement partners to put in a condition that they themselves should use electric vehicles to undertake duties that involve the council.”